From early markers to neuro-developmental mechanisms of autism

A fast growing field, the study of infants at risk because of having an older sibling with autism (i.e. infant sibs) aims to identify the earliest signs of this disorder, which would allow for earlier diagnosis and intervention. More importantly, we argue, these studies offer the opportunity to validate existing neuro-developmental models of autism against experimental evidence. Although autism is mainly seen as a disorder of social interaction and communication, emerging early markers do not exclusively reflect impairments of the “social brain”. Evidence for atypical development of sensory and attentional systems highlight the need to move away from localized deficits to models suggesting brain-wide involvement in autism pathology. We discuss the implications infant sibs findings have for future work into the biology of autism and the development of interventions

Eurosibs: towards robust measurement of infant neurocognitive predictors of Autism across Europe

Autism Spectrum Disorder (ASD) is a neurodevelopmental disorder that affects social communication skills and flexible behaviour. Developing new treatment approaches for ASD requires early identification of the factors that influence later behavioural outcomes. One fruitful research paradigm has been the prospective study of infants with a first degree relative with ASD, who have around a 20% likelihood of developing ASD themselves. Early findings have identified a range of candidate neurocognitive markers for later ASD such as delayed attention shifting or neural responses to faces, but given the early stage of the field most sample sizes are small and replication attempts remain rare. The Eurosibs consortium is a European multisite neurocognitive study of infants with an older sibling with ASD conducted across nine sites in five European countries. In this manuscript, we describe the selection and standardization of our common neurocognitive testing protocol. We report data quality assessments across sites, showing that neurocognitive measures hold great promise for cross-site consistency in diverse populations. We discuss our approach to ensuring robust data analysis pipelines and boosting future reproducibility. Finally, we summarise challenges and opportunities for future multi-site research efforts

A root graph that is locally the line graph of the Petersen graph

AbstractWe construct a root graph on 192 vertices that is locally the line graph of the Petersen graph, a new distance-regular graph on 96 vertices (with intersection array {15,10,1;1,2,15} and automorphism group 24.Sym(6)), and several new strongly regular graphs (with parameters (v,k,λ,μ)=(96,20,4,4) and (96,19,2,4)) and square 2-(96,20,4) designs

Some new strongly regular graphs

We show that three pairwise 4-regular graphs constructed by the second author are members of infinite families

Some new strongly regular graphs

We show that three pairwise 4-regular graphs constructed by the second author are members of infinite families

Assigning Unique Keys to Chemical Compounds for Data Integration: Some Interesting Counter Examples

Integrating data involving chemical structures is simplified when unique identifiers (UIDs) can be associated with chemical structures. For example, these identifiers can be used as database keys. One common approach is to use the Unique SMILES notation introduced in [2]. The Unique SMILES views a chemical structure as a graph with atoms as nodes and bonds as edges and uses a depth first traversal of the graph to generate the SMILES strings. The algorithm establishes a node ordering by using certain symmetry properties of the graphs. In this paper, we present certain molecular graphs for which the algorithm fails to generate UIDs. Indeed, we show that different graphs in the same symmetry class employed by the Unique SMILES algorithm have different Unique SMILES IDs. We tested the algorithm on the National Cancer Institute (NCI) database [7] and found several molecular structures for which the algorithm also failed. We have also written a python script that generates molecular graphs for which the algorithm fails

Transitive permutation groups without semiregular subgroups

A transitive finite permutation group is called elusive if it contains no nontrivial semiregular subgroup. The purpose of the paper is to collect known information about elusive groups. The main results are recursive constructions of elusive permutation groups, using various product operations and affine group constructions. A brief historical introduction and a survey of known elusive groups are also included. In a sequel, Giudici has determined all the quasiprimitive elusive groups.Part of the motivation for studying this class of groups was a conjecture due to Marušic, Jordan and Klin asserting that there is no elusive 2-closed permutation group. It is shown that the constructions given will not build counterexamples to this conjecture

Algebraic methods for chromatic polynomials

AbstractIn this paper we discuss the chromatic polynomial of a ‘bracelet’, when the base graph is a complete graph Kb and arbitrary links L between the consecutive copies are allowed. If there are n copies of the base graph the resulting graph will be denoted by Ln(b). We show that the chromatic polynomial of Ln(b) can be written in the formP(Ln(b);k)=∑ℓ=0b∑π⊢ℓmπ(k)tr(NLπ)n.Here the notation π⊢ℓ means that π is a partition of ℓ, and mπ(k) is a polynomial that does not depend on L. The square matrix NLπ has size bℓnπ, where nπ is the degree of the representation Rπ of Symℓ associated with π.We derive an explicit formula for mπ(k) and describe a method for calculating the matrices NLπ. Examples are given. Finally, we discuss the application of these results to the problem of locating the chromatic zeros